What is the solution to the system of equationsy = 3x - 2 and y = g(x) where g(x) is defined bythe function below?y=g(x)
Answers
we need to write the equation of the graph
it is a parable then the general form is
[tex]y=(x+a)^2+b[/tex]where a move the parable horizontally from the origin (a=negative move to right and a=positive move to left)
and b move the parable vertically from the origin (b=negative move to down and b=positive move to up)
this parable was moving from the origin to the right 2 units and any vertically
then a is -2 and b 0
[tex]y=(x-2)^2[/tex]now we have the system of equations
[tex]\begin{gathered} y=3x-2 \\ y=(x-2)^2 \end{gathered}[/tex]we can replace the y of the first equation on the second and give us
[tex]3x-2=(x-2)^2[/tex]simplify
[tex]3x-2=x^2-4x+4[/tex]we need to solve x but we have terms sith x and x^2 then we can equal to 0 to factor
[tex]\begin{gathered} 3x-2-x^2+4x-4=0 \\ -x^2+7x-6=0 \end{gathered}[/tex]multiply on both sides to remove the negative sign on x^2
[tex]x^2-7x+6=0[/tex]now we use the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a is 1, b is -7 and c is 6
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(6)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]we have two solutions for x
[tex]\begin{gathered} x_1=\frac{7+5}{2}=6 \\ \\ x_2=\frac{7-5}{2}=1 \end{gathered}[/tex]now we replace the values of x on the first equation to find the corresponding values of y
[tex]y=3x-2[/tex]x=6
[tex]\begin{gathered} y=3(6)-2 \\ y=16 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=3(1)-2 \\ y=1 \end{gathered}[/tex]Then we have to pairs of solutions
[tex]\begin{gathered} (6,16) \\ (1,1) \end{gathered}[/tex]where green line is y=3x-2
and red points are the solutions (1,1)and(6,16)
Related Questions
5. Jim owns a farm that has been passed down through his family. The taxassessment on his farm is $399,000. The local tax rate is $6.01 per $100 of theassessment. What is Jim's annual property tax?
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Given:
The assessment value = $399,000.
The local tax rate is $6.01 per $100 of the assessment.
Required:
We need to find the annual property tax.
Explanation:
[tex]A\text{nnual property tax = }\frac{\text{\$6.01}}{100}\times\text{the assessment value}[/tex][tex]A\text{nnual property tax = }\frac{\text{\$6.01}}{100}\times399000[/tex][tex]A\text{nnual property tax = \$23979.90.}[/tex]Final answer:
[tex]A\text{nnual property tax = \$23,979.90.}[/tex]Which of the following points lies on the graph pf the equation 2x + 6y = 6?A. (-3, 0)B. (-2, 9)C. (-3, 2)D. (2, 6)
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Answer:
[tex]C[/tex]Explanation:
Here, we want to get the point that lies on the given graph
To get this, if we substitute the x value and y value into the function, we should get the value on the right-hand side of the equation, which is 6
Let us look at the 3rd option:
[tex]2(-3)\text{ + 6\lparen2\rparen = -6 + 12 = 6}[/tex]From what we can see here, the random choice was correct and thus, C is the correct answer
In a case where this was incorrect, we simply substitute another point and continue this until we arrive at the correct answer choice
8. Find the center of the circle that can be circumscribed about the triangle.y-4-262-224
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The labelled triangle is shown below
The required center is the point where the perpendicular bisectors meet. It is called the circumcenter. We would find it by applying the midpoint method. The midpoint formula is expressed as
midpoint, M(x, y) = (x1 + x2)/2, (y1 + y2)/2
For AB,
x1 = - 4, y1 = 0
x2 = 4, y2 = 0
Midpoint = (- 4 + 4)/2, (0 + 0)/2 = (0, 0)
For AC,
x1 = - 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (- 4 + 0)/2, (0 + 4)/2 = (- 2, 2)
For BC,
x1 = 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (4 + 0)/2, (0 + 4)/2 = (2, 2)
We woulf find the slope of AC
Slope, m = (y2 - y1)/(x2 - x1) = (4 - 0)/(0 - - 4) = 4/(0 + 4) = 4/4
m = 1
Slope of the line per
i need help with math
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1. false= 3 and 5 are corresponding angles
2. false= 7 and 10 are same side exterior angles
3. true
3. true
Help please I want to know how to solve this not just the answer!!
Answers
Answer:
20 overtime hours
Step-by-step explanation:
overtime starts at 40 hours anything after that would be considered overtime
Suppose that you are headed toward a plateau 25.1 meters high. If the angle of elevation to the top of the plateau is 16.5, how far are you from the base of the plateau? meters (Round your answer to the nearest tenth.)
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Suppose that you are headed toward a plateau 25.1 meters high. If the angle of elevation to the top of the plateau is 16.5, how far are you from the base of the plateau? meters (Round your answer to the nearest tenth.)
we have that
tan(16.5)=25.1/x
x is the missing distance
solve for x
x=25.1/tan(16.5)
x=84.7 m
the answer is 84.7 metersScale the rectangle by finding 3A. What are the vertices of the scaled rectangle
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Given A, the matrix that contains the vertices of a rectangle on the plane, calculate 3A as shown below
[tex]3A=3\begin{bmatrix}{1} & {6} & {6} & {1} \\ {1} & {1} & {5} & {5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3*1} & {3*6} & {3*6} & {3*1} \\ {3*1} & {3*1} & {3*5} & {3*5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3} & {18} & {18} & {3} \\ {3} & {3} & {15} & {15} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Where each column of the 4x2 matrix above represents a vertex of the new rectangle; therefore, the 4 vertices are
(3,3), (18,3), (18,15), (3,15). The second option.In the circle below, if AD is a diameter, and the chord BC = 48, find the length of the segment BP.
Answers
Solution
- The length BP is the half of length BC.
- The Diameter is AD and it divides the chord into two equal parts.
- Thus, BP is half of BC. This means that
[tex]\begin{gathered} BP=\frac{BC}{2} \\ \\ BP=\frac{48}{2}=24 \end{gathered}[/tex]Final Answer
BP = 24
5) A bird, flying 25 feet above the sea, spotted a fish swimming 7 feet below the surface. How far did the bird need to go to catch the fish?
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The bird is flying 25 feet above sea surface and the fish is swimming 7 feet below sea surface:
Distance is equal to:
[tex]25-(-7)=25+7=32[/tex]The bird will have to dive 32feet to catch the fish.
Write the equation in equivalent exponential form.log (1) base 6 = 0The equivalent exponential form is(Type an equation.)
Answers
Answer
The equivalent exponential form is 6⁰ = 1
Explanation
Given:
[tex]\log_61=0[/tex]Solution:
Using the definition of a logarithm:
[tex]\begin{gathered} \log_bx=y \\ \\ \Rightarrow b^y=x \end{gathered}[/tex]Thus, the given equation in equivalent exponential form is
[tex]\begin{gathered} \log_61=0 \\ \\ \Rightarrow6^0=1 \end{gathered}[/tex]The equivalent exponential form is 6⁰ = 1
Sherman counted up all his hockey player cards and realized he had 200. He recently purchased a book to organize them that holds 20 cards on a page. If he puts 2 pages in a section, how many sections will he have in his book? Select the expression that represents the problem above. a) 200 = 20 = 2 b) 200 x 20 x 2 c) 200 20 x 2 d) 200 x 20 = 2
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The total number of hockey cards is 200
The number of cards on a page is 20.
The number of pages in a section is 2.
Let there are x number of sections in a book. So number of cards on the x sections should be equal to total number of cards.
Determine the number of cards on the sections.
[tex]20\times2\times x[/tex]
The total number of hocker card is equal to 200. So equation is,
[tex]200=20\times2\times x[/tex]Find each of the following products by first using division and then multiplication each will be a while number answer
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so
[tex]\begin{gathered} \frac{11}{4}\text{ x 8=11 x 2=22 by multiplication} \\ \end{gathered}[/tex]now by division, we can write
[tex]\frac{11}{4}\text{ }\div\frac{1}{8}=22\text{ }[/tex]when we divide by a fraction, we multiply by its reciprocal
2) Elena has some bottles of water that each holds 17 fluid ounces. a) Write an equation that relates the number of bottles of water (b) to the total volume of water (w) in fluid ounces. b) How much water is in 51 bottles? Show your work. c) How many bottles does it take to hold 51 fluid ounces of water? Show your work.
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Answer:
(a)
Since each bottle holds 17 fluid ounces, then if b is the number of bottles of water and w is the total volume of water in fluid ounces we can set the following equation:
[tex]w=17b\text{.}[/tex](b)
Now, if b=51,
[tex]w=17\times51=867.[/tex]Therefore, in 51 bottles there are 867 fluid ounces.
(c)
If w=51, solving for b we get:
[tex]\begin{gathered} 51=17b, \\ \frac{51}{17}=b, \\ b=3. \end{gathered}[/tex]
Therefore, it would take 3 bottles to hold 51 fluid ounces.
The equation of the line parallel to y = 3x + 8 that passes through the point (4, 5) is
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To answer this question, we need to remember that a line is parallel to another one if its slopes are the same. A line parallel to y = 3x + 8 must has a slope, m = 3.
Now, to find the parallel line, we can use the point-slope form of the line equation as follows:
1. The point for which the line passes through is (4, 5):
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
(4, 5) ---> x1 = 4, y1 = 5
m = 3
[tex]y-5=3(x-4)\Rightarrow y-5=3x-12[/tex]Then
[tex]y=3x-12+5\Rightarrow y=3x-7[/tex]Therefore, the equation of the line parallel to y = 3x + 8 that passes through the point (4, 5) is y = 3x - 7.
ctice 3.4.PS-19 Use the expression 6.5u - (10 =2) + 13 to answer 9–10. 9. Which part of the expression represents a quotient? Describe its parts. 10. Which part of the expression represents a product of two factors? Describe its p 9. The part of the expression that represents a quotient is (10=2). (Use the operation symbols in the math palette as needed. Do not simplify.) In this quotient, 6 is the dividend and 5U is the divisor
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10 is the dividend while 2 is the divisor
Here, from the part that represents the quotient, we want to get the divisor and the dividend
From the question, the part that represents a quotient is given as;
[tex]\frac{10}{2}[/tex]Now, when we speak of the dividend, we mean the numerator of the fraction, and when we talk of the divisor, we are talking about the denominator
In simpler terms, what we want to divide is the dividend while what we are dividing with is the divisor
With respect to the given question, 10 is the dividend while 2 is the divisor
A laptop has ablisted price of $739.98 befire tax. If the sales tax rate is 8.75%, find the total cost of the laptop with sales tax included.
Answers
Total cost of laptop after sales tax is included = $804.73
Explanation:
price before sales tax = $739.98
Sales tax rate = 8.75%
Total cost of laptop after sales tax = $739.98 × (100% + 8.75%)
= $739.98 × (1 + 0.0875)
= 739.98 × 1.0875
= $804.73
Total cost of laptop after sales tax is included= $804.73
A sample was done , collecting the data below. Calculate the standard deviation,to one decimal place
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By definition, the standard deviation is
[tex]\sigma = \sqrt{\frac{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}{n}}[/tex]It seems hard so let's do it step by step, first, let's find the mean of the data
[tex]\begin{gathered} \bar{x}=\frac{24+29+2+21+9}{5} \\ \\ \bar{x}=17 \end{gathered}[/tex]Now we have the mean value, let's do each value of the set minus the mean value
[tex]\begin{gathered} x_1-\bar{x}=24-17=7 \\ \\ x_2-\bar{x}=29-17=12 \\ \\ x_3-\bar{x}=2-17=-15 \\ \\ x_4-\bar{x}=29-17=4 \\ \\ x_4-\bar{x}=9-17=-8 \end{gathered}[/tex]Now we have the difference between each element and the mean value, let's do the square of all values
[tex]\begin{gathered} (x_1-\bar{x})^2=7^2=49 \\ \\ (x_2-\bar{x})^2=12^2=144 \\ \\ (x_3-\bar{x})^2=(-15)^2=225 \\ \\ (x_4-\bar{x})^2=4^2=16 \\ \\ (x_5-\bar{x})^2=(-8)^2=64 \end{gathered}[/tex]Now we have the square of the difference we sum them
[tex]\begin{gathered} \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=\left(x_1-\bar{x}\right)^2+\left(x_2-\bar{x}\right)^2+\left(x_3-\bar{x}\right)^2+\left(x_4-\bar{x}\right)^2+\left(x_5-\bar{x}\right)^2 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=49+144+225+16+64 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=498 \end{gathered}[/tex]Now we have the sum we must divide by the number of elements, in that case, 5 elements
[tex]\frac{\sum_{i=1}^5\left(x_i-\bar{x}\right)^2}{5}=99.6[/tex]Now we take the square root of that value to have the standard deviation!
[tex]\sigma=\sqrt{99.6}=9.979[/tex]We write it using only one decimal the result would be
[tex]\sigma=9.9[/tex]With no rounding.
Final answer:
[tex]\sigma=9.9[/tex]The following picture has the question that has me troubled can you show me how to get to the answer
Answers
Given that:
[tex]f(x)=\sqrt[]{x},x_0=8,dx=0.07[/tex]Find the change.
[tex]\begin{gathered} \nabla f=f(8+\text{0}.07)-f(8) \\ =f(8.07)-f(8) \\ =\sqrt[]{8.07}-\sqrt[]{8} \\ =0.0123474175 \end{gathered}[/tex]Find the estimate value.
[tex]\begin{gathered} df=\frac{1}{2\sqrt[]{8}}\cdot0.07 \\ =0.0123743687 \end{gathered}[/tex]Determine the approximate error.
[tex]\begin{gathered} |\nabla f-df|=|0.0123474175-0.0123743687| \\ =0.0000269512 \\ \approx0.00002 \end{gathered}[/tex]Option B is correct.
What is the measure of angle B in this triangle?
Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
First, you add the degrees available to you, next, you need to count the variable and add them together, in this case, your problem should show, 40+20-30 for your degrees, which is 30 degrees. Next, you have an "x" and a "2x," therefore you add them together to get 3x. After doing this, you get to your 2-step equation, which should look like 30 + 3x = 180. You get 180 because that is the length of the triangle, it should always be 180. You can now start by subtracting 180 - 30, we switch the + and - when doing the first part. Now, you should have gotten, 150, with 150 you can divide it by 3, you divided by 3 because you switch the division and the multiplication, now you do 150 divided by 3, which is 50. YOUR ANSWER IS: x = 50.
Pls help!!!! asapppp
Answers
The percentage decrease in the price of the stock is 0.72%
The initial price of the technology stock = $9.66
The new price of the technology stock = $9.59
The decrease in price = The initial price of the technology stock - The new price of the technology stock
Substitute the values in the equation
= 9.66 - 9.59
Subtract the terms
= $0.07
The percentage of decrease in price = (The decrease in price / The initial price of the technology stock) × 100
Substitute the values in the equation
= (0.07 / 9.66) × 100
= 0.72 %
Hence, the percentage decrease in the price of the stock is 0.72%
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A blimp provides aerial television views of a tennis game. The television camera sights the stadium at 14° angle of depression. The altitude of the blimp is 300m . What is the line-of sight distance from the television camera to the base of the stadium ? Round to the nearest hundred meters.
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Notice that with the information given, we can make a simple schematics of a right angle triangle for which we know an acute angle, a leg, and are asked to find the other leg of the triangle (or the hypotenuse, since the word "line of sight is not used properly in the text of the problem). The schematics is shown below:
The other leg of the right triangle is pictured in red in the image, if it is what the problem is asking (LINE OF SIGHT DISTANCE, which is always understood as a horizontal reference).
So we can use the tangent function to solve this case, as shown below
[tex]\begin{gathered} \tan (14\circ)=\frac{300}{d} \\ d=\frac{300}{\tan (14)}\approx1203.23 \end{gathered}[/tex]which tells us that the horizontal distance between camera and end of the field is approximately 1203.23 meters.
In the case that the problem is asking for the slant distance between the camera and the end of the field, we need to find the HYPOTENUSE of the right angle triangle (pictured in orange in the image above), and in such case we use the sine function as shown below:
[tex]\begin{gathered} \sin (14)=\frac{300}{\text{hyp}} \\ \text{hyp}=\frac{300}{\sin (14)}\approx1240.07 \end{gathered}[/tex]Which tells us that the slant distance between camera and the end of the field is about 1240.7 meters
From the drawing you sent, it looks more like the teacher may be asking for the slant distance. So please use the second answer : 1240.7 meters.
Please remind you teacher that the standard use of "line of sight" is to represent the horizontal line from which the angle of elevation or angle of depression is measured. So it is not appropriate to use the term in the context it has been used.
Given: The base of the pyramid is a regular pentagon.13 ft5 ftWhat is the lateral area of the pyramid?O 100108.3O 150O162.5
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The Solution.
The lateral area of the given pyramid is the total area of the 5 triangular faces of the pyramid.
So, we have
[tex]\text{Lateral Area of the pyramid = 5(}\frac{1}{2}bh)[/tex]In this case,
[tex]b=5\text{ ft, h=13 ft}[/tex]Substituting these values in the formula above, we get
[tex]\text{Lateral Area of the pyramid = 5}\times\frac{1}{2}\times5\times13[/tex][tex]\text{Lateral Area of the pyramid = }\frac{25\times13}{2}=\frac{325}{2}=162.5ft^2[/tex]Hence, the correct answer is 162.5 square feet (option 4).
Drag and drop the angles and line segments into the correct category to identify those that are chords, Inscribed angles, and central angles in the figure. The center of the circle is C. C E F DEF EF DCF DE Chords Inscribed Angles Central Angles
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Given data:
The given figure is shown.
The chords are,
EF
DE
The inscribed angle is ∠DEF.
The central angle is ∠DCF.
Thus, EF and DE are chords. ∠DEF is inscribed angle, and ∠DCF is cenral angle.
By visual inspection, determine the best-fitting regression model for thescatterplot.
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From visual inspection it is clear that the best fitting regression model for this scatterplot is linear.
In the graph we can clearly see that the points form an almost straight line with a negative slope.
Now we know that a straight line has an equation of y = mx + c
The regression equation will be Y = aX + b which is a linear equation.
The mathematical figure known as a scatter plot, also known as a scatter graph, scatter chart, scattergram, a scatter diagram, uses Cartesian coordinates to display values in typically two variables for a set of data.
One more variable can be shown if a points are color, shape, and size coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable, and its position on the vertical axis by the value of the other variable.
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3(4x+3)-12how do you simplify
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By following the order of operations, we need to evaluate first the multiplication of 3 and (4x+3) by using the distributive property.
[tex]\begin{gathered} 3(4x+3)-12\text{ (given)} \\ \\ \text{apply the distributive property} \\ =(3\cdot4x+3\cdot3)-12 \\ =12x+9-12 \end{gathered}[/tex]After that, combine like terms, we see from the previous solution that 12x has no other like terms, and it will remain as is. 9 and 12 however are both constant, and should be simplified
[tex]\begin{gathered} 12x+9-12 \\ =12x-3 \end{gathered}[/tex]Therefore, 3(4x+3) - 12, when simplified is 12x - 3.
What is the solution to the inequality 2-2x > -20
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To determine the solution for the given inequality, you have to solve it for x:
[tex]2-2x>-20[/tex]First, pass 2 to the right side of the inequality by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 2-2-2x>-20-2 \\ -2x>-22 \end{gathered}[/tex]Next, note that the x-term is multiplied by "-2", to reach the value of x you have to cancel the said multiplication. For this, you have to divide both sides of the expression by "-2"
Now, keep in mind, that when you divide or multiply an inequality by a negative number, the direction of the inequality gets inversed. This means that the symbol "greater than, >" will tur into the symbol "less than. <":
[tex]\begin{gathered} -\frac{2x}{-2}<-\frac{22}{-2} \\ x<11 \end{gathered}[/tex]The solution for this inequality will be the values of x less than 11, symbolically: x < 11
Caitlin read a book. She started reading at 9:45 a.m. and ended at 10:37 a.m. How did How many minutes did Caitlin read?
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To calculate the number of minutes, we have to convert the hours to minutes or we can calculate the difference between the starting and ending times to a fixed hour.
In this case, we will use the second approach.
We will use 10:00 am as the fixed hour.
Then, if she started reading at 9:45 am, 15 minutes had passed until 10 am.
If she ended reading at 10:37 am, 37 minutes passed from 10 am.
Then, we can add the two segments:
[tex]T=15+37=52\min [/tex]Answer: she read 52 minutes.
The area of this rectangle is 15ft^2. Write and equation and solve it to find y
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The Area of a rectangle can be calculated by using the formula:
[tex]A=L\times W[/tex]Where A is the area, L is the length and W is the width.
By replacing the given values, your equation will be:
[tex]15ft^2=y\times3ft[/tex]Do the next steps to find the value of y:
[tex]\begin{gathered} \text{Divide both sides by 3 ft} \\ \frac{15ft^2}{3ft}=y\times\frac{3ft}{3ft}\text{ } \\ \text{Simplify and reorder terms} \\ 5ft=y \\ y=5ft \end{gathered}[/tex]Thus, the value of y is 5 ft.
a is the midpoint of segment XY.find the value of x and the length of XY
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ANSWER
x = 3, XY = 18
EXPLANATION
We have that A is the midpoint of XY. It means that A divides XY into 2 equal parts.
This means that:
XA = AY
We have that:
XA = 3x
AY = 5x - 6
=> 3x = 5x - 6
Collect like terms:
3x - 5x = -6
-2x = -6
Divide through by -2:
x = -6 / -2
x = 3
That is the value of x.
Since A is the midpoint of XY and XA = AY, then:
XY = 2XA or XAY
So:
XY = 2XA
XY = 2 * 3x = 2 * 3(3)
XY = 2 * 9
XY = 18
That is the value of XY.
Complete all of the following steps to for each problem below.Write C for combine (add) or D for difference (D)Write (+) if the sum will be positive or (-) if the sum will be negativeDetermine the final answer8 + -2 = -9 + -12 = -35 + 25 = -19 + 40 =
Answers
Answer:
+6
Step-by-step explanation:
We have to solve the following expression:
8 + (-2)
The + sign before the parenthesis means that the signal of the terms inside the parenthesis stay the same. So
8 + (-2) = 8 - 2 = +6
The answer is +6.